Grandmaster Alexandra Kosteniuk ponders the question in this chess video tutorial, "Should White resign or play on?" This chess example that will get you on your way to being a Grandmaster yourself is from a study in 1922 by Kraemer.

Should White resign, or can he still draw this chess endgame? Here, you find that White can save the game, by acquiring a stalemate.

Wikipedia states that a stalemate is a situation in chess where the player whose turn it is to move has no legal moves but is not in check. Stalemate ends the game, with the result a draw. Often during the endgame the player who is behind in material seeks stalemate in order to avoid losing the game